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Linear and projective representations of symmetric groups /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Linear and projective representations of symmetric groups // Alexander Kleshchev.
其他題名:	Linear & Projective Representations of Symmetric Groups
作者:	Kleshchëv, A. S.
面頁冊數:	1 online resource (xiv, 277 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Geometry, Projective. -
電子資源:	https://doi.org/10.1017/CBO9780511542800
ISBN:	9780511542800 (ebook)

Linear and projective representations of symmetric groups /
Kleshchëv, A. S.

Linear and projective representations of symmetric groups /Linear & Projective Representations of Symmetric GroupsAlexander Kleshchev. - 1 online resource (xiv, 277 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;163. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Notation and generalities --1.

The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject.

ISBN: 9780511542800 (ebook)Subjects--Topical Terms:

672454
Geometry, Projective.

LC Class. No.: QA176 / .K56 2005

Dewey Class. No.: 512.5

Linear and projective representations of symmetric groups /
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245 1 0 $a Linear and projective representations of symmetric groups / $c Alexander Kleshchev.
246 3 $a Linear & Projective Representations of Symmetric Groups
264 1 $a Cambridge : $b Cambridge University Press, $c 2005.
300 $a 1 online resource (xiv, 277 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
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338 $a online resource $b cr $2 rdacarrier
490 1 $a Cambridge tracts in mathematics ; $v 163
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $g 1. $t Notation and generalities -- $g 2. $t Symmetric groups I -- $g 3. $t Degenerate affine Hecke algebra -- $g 4. $t First results on H[subscript n]-modules -- $g 5. $t Crystal operators -- $g 6. $t Character calculations -- $g 7. $t Integral representations and cyclotomic Hecke algebras -- $g 8. $t Functors e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] -- $g 9. $t Construction of U[subscript z][superscript +] and irreducible modules -- $g 10. $t Identification of the crystal -- $g 11. $t Symmetric groups II -- $g 12. $t Generalities on superalgebra -- $g 13. $t Sergeev superalgebras -- $g 14. $t Affine Sergeev superalgebras -- $g 15. $t Integral representations and cyclotomic Sergeev algebras -- $g 16. $t First results on X[subscript n]-modules -- $g 17. $t Crystal operators for X[subscript n] -- $g 18. $t Character calculations for X[subscript n] -- $g 19. $t Operators e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] -- $g 20. $t Construction of U[subscript z][superscript +] and irreducible modules -- $g 21. $t Identification of the crystal -- $g 22. $t Double covers.
520 $a The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject.
650 0 $a Geometry, Projective. $3 672454
650 0 $a Algebras, Linear. $3 528115
650 0 $a Linear algebraic groups. $3 672180
650 0 $a Superalgebras. $3 672284
650 0 $a Hecke algebras. $3 788111
650 0 $a Modular representations of groups. $3 907670
650 0 $a Representations of groups. $3 672181
650 0 $a Symmetry groups. $3 527839
776 0 8 $i Print version: $z 9780521837033
830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511542800